Strongly coupled quantum field theory
Abstract
I analyze numerically a two-dimensional λϕ4 theory showing that in the limit of a strong coupling λ→∞ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M. Frasca, Phys. Rev. A 58, 3439 (1998)PLRAAN1050-294710.1103/PhysRevA.58.3439], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this nonlinear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, I built a strongly coupled quantum field theory for a λϕ4 interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of space-time. The agreement with the Lehmann-Källen representation of the perturbation series is then shown at the first order.
- Publication:
-
Physical Review D
- Pub Date:
- January 2006
- DOI:
- 10.1103/PhysRevD.73.027701
- arXiv:
- arXiv:hep-th/0511068
- Bibcode:
- 2006PhRvD..73b7701F
- Keywords:
-
- 11.15.Me;
- 02.60.Lj;
- Strong-coupling expansions;
- Ordinary and partial differential equations;
- boundary value problems;
- High Energy Physics - Theory;
- Condensed Matter - Other Condensed Matter;
- High Energy Physics - Phenomenology;
- Mathematical Physics
- E-Print:
- 6 pages, 4 figures. Version accepted for publication in Physical Review D. Added erratum to appear on PRD: just corrected eq.(5)